text: //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  //
  // This file contains some functions that are useful for math stuff.
  //
  //===----------------------------------------------------------------------===//
  
  #ifndef LLVM_SUPPORT_MATHEXTRAS_H
  #define LLVM_SUPPORT_MATHEXTRAS_H
  
  #include "llvm/Compiler.h"
  #include <cstdint>
  #include <algorithm>
  #include <cassert>
  #include <cmath>
  #include <cstring>
  #include <type_traits>
  #include <limits>
  
  #ifdef _MSC_VER
  #include <intrin.h>
  #endif
  
  namespace llvm {
  /// \brief The behavior an operation has on an input of 0.
  enum ZeroBehavior {
    /// \brief The returned value is undefined.
    ZB_Undefined,
    /// \brief The returned value is numeric_limits<T>::max()
    ZB_Max,
    /// \brief The returned value is numeric_limits<T>::digits
    ZB_Width
  };
  
  namespace detail {
  template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
    static std::size_t count(T Val, ZeroBehavior) {
      if (!Val)
        return std::numeric_limits<T>::digits;
  
      // Bisection method.
      std::size_t ZeroBits = 0;
      for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
        T Tmp = Val >> Shift;
        if (Tmp)
          Val = Tmp;
        else
          ZeroBits |= Shift;
      }
      return ZeroBits;
    }
  };
  
  #if __GNUC__ >= 4 || defined(_MSC_VER)
  template <typename T> struct LeadingZerosCounter<T, 4> {
    static std::size_t count(T Val, ZeroBehavior ZB) {
      if (ZB != ZB_Undefined && Val == 0)
        return 32;
  
  #if __has_builtin(__builtin_clz) || LLVM_GNUC_PREREQ(4, 0, 0)
      return __builtin_clz(Val);
  #elif defined(_MSC_VER)
      unsigned long Index;
      _BitScanReverse(&Index, Val);
      return Index ^ 31;
  #endif
    }
  };
  
  #if !defined(_MSC_VER) || defined(_M_X64)
  template <typename T> struct LeadingZerosCounter<T, 8> {
    static std::size_t count(T Val, ZeroBehavior ZB) {
      if (ZB != ZB_Undefined && Val == 0)
        return 64;
  
  #if __has_builtin(__builtin_clzll) || LLVM_GNUC_PREREQ(4, 0, 0)
      return __builtin_clzll(Val);
  #elif defined(_MSC_VER)
      unsigned long Index;
      _BitScanReverse64(&Index, Val);
      return Index ^ 63;
  #endif
    }
  };
  #endif
  #endif
  } // namespace detail
  
  /// \brief Count number of 0's from the most significant bit to the least
  ///   stopping at the first 1.
  ///
  /// Only unsigned integral types are allowed.
  ///
  /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
  ///   valid arguments.
  template <typename T>
  std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
    static_assert(std::numeric_limits<T>::is_integer &&
                      !std::numeric_limits<T>::is_signed,
                  "Only unsigned integral types are allowed.");
    return detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
  }
  
  /// \brief Get the index of the last set bit starting from the least
  ///   significant bit.
  ///
  /// Only unsigned integral types are allowed.
  ///
  /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are
  ///   valid arguments.
  template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) {
    if (ZB == ZB_Max && Val == 0)
      return std::numeric_limits<T>::max();
  
    // Use ^ instead of - because both gcc and llvm can remove the associated ^
    // in the __builtin_clz intrinsic on x86.
    return countLeadingZeros(Val, ZB_Undefined) ^
           (std::numeric_limits<T>::digits - 1);
  }
  
  /// \brief Macro compressed bit reversal table for 256 bits.
  ///
  /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable
  static const unsigned char BitReverseTable256[256] = {
  #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64
  #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16)
  #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4)
    R6(0), R6(2), R6(1), R6(3)
  #undef R2
  #undef R4
  #undef R6
  };
  
  /// \brief Reverse the bits in \p Val.
  template <typename T>
  T reverseBits(T Val) {
    unsigned char in[sizeof(Val)];
    unsigned char out[sizeof(Val)];
    std::memcpy(in, &Val, sizeof(Val));
    for (unsigned i = 0; i < sizeof(Val); ++i)
      out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]];
    std::memcpy(&Val, out, sizeof(Val));
    return Val;
  }
  
  // NOTE: The following support functions use the _32/_64 extensions instead of
  // type overloading so that signed and unsigned integers can be used without
  // ambiguity.
  
  /// Hi_32 - This function returns the high 32 bits of a 64 bit value.
  inline uint32_t Hi_32(uint64_t Value) {
    return static_cast<uint32_t>(Value >> 32);
  }
  
  /// Lo_32 - This function returns the low 32 bits of a 64 bit value.
  inline uint32_t Lo_32(uint64_t Value) {
    return static_cast<uint32_t>(Value);
  }
  
  /// Make_64 - This functions makes a 64-bit integer from a high / low pair of
  ///           32-bit integers.
  inline uint64_t Make_64(uint32_t High, uint32_t Low) {
    return ((uint64_t)High << 32) | (uint64_t)Low;
  }
  
  /// isInt - Checks if an integer fits into the given bit width.
  template<unsigned N>
  inline bool isInt(int64_t x) {
    return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1)));
  }
  // Template specializations to get better code for common cases.
  template<>
  inline bool isInt<8>(int64_t x) {
    return static_cast<int8_t>(x) == x;
  }
  template<>
  inline bool isInt<16>(int64_t x) {
    return static_cast<int16_t>(x) == x;
  }
  template<>
  inline bool isInt<32>(int64_t x) {
    return static_cast<int32_t>(x) == x;
  }
  
  /// isShiftedInt<N,S> - Checks if a signed integer is an N bit number shifted
  ///                     left by S.
  template<unsigned N, unsigned S>
  inline bool isShiftedInt(int64_t x) {
    return isInt<N+S>(x) && (x % (1<<S) == 0);
  }
  
  /// isUInt - Checks if an unsigned integer fits into the given bit width.
  template<unsigned N>
  inline bool isUInt(uint64_t x) {
    return N >= 64 || x < (UINT64_C(1)<<(N));
  }
  // Template specializations to get better code for common cases.
  template<>
  inline bool isUInt<8>(uint64_t x) {
    return static_cast<uint8_t>(x) == x;
  }
  template<>
  inline bool isUInt<16>(uint64_t x) {
    return static_cast<uint16_t>(x) == x;
  }
  template<>
  inline bool isUInt<32>(uint64_t x) {
    return static_cast<uint32_t>(x) == x;
  }
  
  /// isShiftedUInt<N,S> - Checks if a unsigned integer is an N bit number shifted
  ///                     left by S.
  template<unsigned N, unsigned S>
  inline bool isShiftedUInt(uint64_t x) {
    return isUInt<N+S>(x) && (x % (1<<S) == 0);
  }
  
  /// Gets the maximum value for a N-bit unsigned integer.
  inline uint64_t maxUIntN(uint64_t N) {
    assert(N > 0 && N <= 64 && "integer width out of range");
  
    return (UINT64_C(1) << N) - 1;
  }
  
  /// Gets the minimum value for a N-bit signed integer.
  inline int64_t minIntN(int64_t N) {
    assert(N > 0 && N <= 64 && "integer width out of range");
  
    return -(INT64_C(1)<<(N-1));
  }
  
  /// Gets the maximum value for a N-bit signed integer.
  inline int64_t maxIntN(int64_t N) {
    assert(N > 0 && N <= 64 && "integer width out of range");
  
    return (INT64_C(1)<<(N-1)) - 1;
  }
  
  /// isUIntN - Checks if an unsigned integer fits into the given (dynamic)
  /// bit width.
  inline bool isUIntN(unsigned N, uint64_t x) {
    return N >= 64 || x <= maxUIntN(N);
  }
  
  /// isIntN - Checks if an signed integer fits into the given (dynamic)
  /// bit width.
  inline bool isIntN(unsigned N, int64_t x) {
    return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N));
  }
  
  /// isMask_32 - This function returns true if the argument is a non-empty
  /// sequence of ones starting at the least significant bit with the remainder
  /// zero (32 bit version).  Ex. isMask_32(0x0000FFFFU) == true.
  inline bool isMask_32(uint32_t Value) {
    return Value && ((Value + 1) & Value) == 0;
  }
  
  /// isMask_64 - This function returns true if the argument is a non-empty
  /// sequence of ones starting at the least significant bit with the remainder
  /// zero (64 bit version).
  inline bool isMask_64(uint64_t Value) {
    return Value && ((Value + 1) & Value) == 0;
  }
  
  /// isShiftedMask_32 - This function returns true if the argument contains a
  /// non-empty sequence of ones with the remainder zero (32 bit version.)
  /// Ex. isShiftedMask_32(0x0000FF00U) == true.
  inline bool isShiftedMask_32(uint32_t Value) {
    return Value && isMask_32((Value - 1) | Value);
  }
  
  /// isShiftedMask_64 - This function returns true if the argument contains a
  /// non-empty sequence of ones with the remainder zero (64 bit version.)
  inline bool isShiftedMask_64(uint64_t Value) {
    return Value && isMask_64((Value - 1) | Value);
  }
  
  /// isPowerOf2_32 - This function returns true if the argument is a power of
  /// two > 0. Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.)
  inline bool isPowerOf2_32(uint32_t Value) {
    return Value && !(Value & (Value - 1));
  }
  
  /// isPowerOf2_64 - This function returns true if the argument is a power of two
  /// > 0 (64 bit edition.)
  inline bool isPowerOf2_64(uint64_t Value) {
    return Value && !(Value & (Value - int64_t(1L)));
  }
  
  /// \brief Count the number of ones from the most significant bit to the first
  /// zero bit.
  ///
  /// Ex. CountLeadingOnes(0xFF0FFF00) == 8.
  /// Only unsigned integral types are allowed.
  ///
  /// \param ZB the behavior on an input of all ones. Only ZB_Width and
  /// ZB_Undefined are valid arguments.
  template <typename T>
  std::size_t countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) {
    static_assert(std::numeric_limits<T>::is_integer &&
                      !std::numeric_limits<T>::is_signed,
                  "Only unsigned integral types are allowed.");
    return countLeadingZeros(~Value, ZB);
  }
  
  namespace detail {
  template <typename T, std::size_t SizeOfT> struct PopulationCounter {
    static unsigned count(T Value) {
      // Generic version, forward to 32 bits.
      static_assert(SizeOfT <= 4, "Not implemented!");
  #if __GNUC__ >= 4
      return __builtin_popcount(Value);
  #else
      uint32_t v = Value;
      v = v - ((v >> 1) & 0x55555555);
      v = (v & 0x33333333) + ((v >> 2) & 0x33333333);
      return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
  #endif
    }
  };
  
  template <typename T> struct PopulationCounter<T, 8> {
    static unsigned count(T Value) {
  #if __GNUC__ >= 4
      return __builtin_popcountll(Value);
  #else
      uint64_t v = Value;
      v = v - ((v >> 1) & 0x5555555555555555ULL);
      v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL);
      v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
      return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56);
  #endif
    }
  };
  } // namespace detail
  
  /// \brief Count the number of set bits in a value.
  /// Ex. countPopulation(0xF000F000) = 8
  /// Returns 0 if the word is zero.
  template <typename T>
  inline unsigned countPopulation(T Value) {
    static_assert(std::numeric_limits<T>::is_integer &&
                      !std::numeric_limits<T>::is_signed,
                  "Only unsigned integral types are allowed.");
    return detail::PopulationCounter<T, sizeof(T)>::count(Value);
  }
  
  /// Log2 - This function returns the log base 2 of the specified value
  inline double Log2(double Value) {
  #if defined(__ANDROID_API__) && __ANDROID_API__ < 18
    return __builtin_log(Value) / __builtin_log(2.0);
  #else
    return std::log2(Value);
  #endif
  }
  
  /// Log2_32 - This function returns the floor log base 2 of the specified value,
  /// -1 if the value is zero. (32 bit edition.)
  /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2
  inline unsigned Log2_32(uint32_t Value) {
    return 31 - countLeadingZeros(Value);
  }
  
  /// Log2_64 - This function returns the floor log base 2 of the specified value,
  /// -1 if the value is zero. (64 bit edition.)
  inline unsigned Log2_64(uint64_t Value) {
    return 63 - countLeadingZeros(Value);
  }
  
  /// Log2_32_Ceil - This function returns the ceil log base 2 of the specified
  /// value, 32 if the value is zero. (32 bit edition).
  /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3
  inline unsigned Log2_32_Ceil(uint32_t Value) {
    return 32 - countLeadingZeros(Value - 1);
  }
  
  /// Log2_64_Ceil - This function returns the ceil log base 2 of the specified
  /// value, 64 if the value is zero. (64 bit edition.)
  inline unsigned Log2_64_Ceil(uint64_t Value) {
    return 64 - countLeadingZeros(Value - 1);
  }
  
  /// GreatestCommonDivisor64 - Return the greatest common divisor of the two
  /// values using Euclid's algorithm.
  inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) {
    while (B) {
      uint64_t T = B;
      B = A % B;
      A = T;
    }
    return A;
  }
  
  /// BitsToDouble - This function takes a 64-bit integer and returns the bit
  /// equivalent double.
  inline double BitsToDouble(uint64_t Bits) {
    union {
      uint64_t L;
      double D;
    } T;
    T.L = Bits;
    return T.D;
  }
  
  /// BitsToFloat - This function takes a 32-bit integer and returns the bit
  /// equivalent float.
  inline float BitsToFloat(uint32_t Bits) {
    union {
      uint32_t I;
      float F;
    } T;
    T.I = Bits;
    return T.F;
  }
  
  /// DoubleToBits - This function takes a double and returns the bit
  /// equivalent 64-bit integer.  Note that copying doubles around
  /// changes the bits of NaNs on some hosts, notably x86, so this
  /// routine cannot be used if these bits are needed.
  inline uint64_t DoubleToBits(double Double) {
    union {
      uint64_t L;
      double D;
    } T;
    T.D = Double;
    return T.L;
  }
  
  /// FloatToBits - This function takes a float and returns the bit
  /// equivalent 32-bit integer.  Note that copying floats around
  /// changes the bits of NaNs on some hosts, notably x86, so this
  /// routine cannot be used if these bits are needed.
  inline uint32_t FloatToBits(float Float) {
    union {
      uint32_t I;
      float F;
    } T;
    T.F = Float;
    return T.I;
  }
  
  /// MinAlign - A and B are either alignments or offsets.  Return the minimum
  /// alignment that may be assumed after adding the two together.
  inline uint64_t MinAlign(uint64_t A, uint64_t B) {
    // The largest power of 2 that divides both A and B.
    //
    // Replace "-Value" by "1+~Value" in the following commented code to avoid
    // MSVC warning C4146
    //    return (A | B) & -(A | B);
    return (A | B) & (1 + ~(A | B));
  }
  
  /// \brief Aligns \c Addr to \c Alignment bytes, rounding up.
  ///
  /// Alignment should be a power of two.  This method rounds up, so
  /// alignAddr(7, 4) == 8 and alignAddr(8, 4) == 8.
  inline uintptr_t alignAddr(const void *Addr, size_t Alignment) {
    assert(Alignment && isPowerOf2_64((uint64_t)Alignment) &&
           "Alignment is not a power of two!");
  
    assert((uintptr_t)Addr + Alignment - 1 >= (uintptr_t)Addr);
  
    return (((uintptr_t)Addr + Alignment - 1) & ~(uintptr_t)(Alignment - 1));
  }
  
  /// \brief Returns the necessary adjustment for aligning \c Ptr to \c Alignment
  /// bytes, rounding up.
  inline size_t alignmentAdjustment(const void *Ptr, size_t Alignment) {
    return alignAddr(Ptr, Alignment) - (uintptr_t)Ptr;
  }
  
  /// NextPowerOf2 - Returns the next power of two (in 64-bits)
  /// that is strictly greater than A.  Returns zero on overflow.
  inline uint64_t NextPowerOf2(uint64_t A) {
    A |= (A >> 1);
    A |= (A >> 2);
    A |= (A >> 4);
    A |= (A >> 8);
    A |= (A >> 16);
    A |= (A >> 32);
    return A + 1;
  }
  
  /// Returns the power of two which is less than or equal to the given value.
  /// Essentially, it is a floor operation across the domain of powers of two.
  inline uint64_t PowerOf2Floor(uint64_t A) {
    if (!A) return 0;
    return 1ull << (63 - countLeadingZeros(A, ZB_Undefined));
  }
  
  /// Returns the next integer (mod 2**64) that is greater than or equal to
  /// \p Value and is a multiple of \p Align. \p Align must be non-zero.
  ///
  /// If non-zero \p Skew is specified, the return value will be a minimal
  /// integer that is greater than or equal to \p Value and equal to
  /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than
  /// \p Align, its value is adjusted to '\p Skew mod \p Align'.
  ///
  /// Examples:
  /// \code
  ///   alignTo(5, 8) = 8
  ///   alignTo(17, 8) = 24
  ///   alignTo(~0LL, 8) = 0
  ///   alignTo(321, 255) = 510
  ///
  ///   alignTo(5, 8, 7) = 7
  ///   alignTo(17, 8, 1) = 17
  ///   alignTo(~0LL, 8, 3) = 3
  ///   alignTo(321, 255, 42) = 552
  /// \endcode
  inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
    Skew %= Align;
    return (Value + Align - 1 - Skew) / Align * Align + Skew;
  }
  
  /// Returns the largest uint64_t less than or equal to \p Value and is
  /// \p Skew mod \p Align. \p Align must be non-zero
  inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) {
    Skew %= Align;
    return (Value - Skew) / Align * Align + Skew;
  }
  
  /// Returns the offset to the next integer (mod 2**64) that is greater than
  /// or equal to \p Value and is a multiple of \p Align. \p Align must be
  /// non-zero.
  inline uint64_t OffsetToAlignment(uint64_t Value, uint64_t Align) {
    return alignTo(Value, Align) - Value;
  }
  
  /// SignExtend32 - Sign extend B-bit number x to 32-bit int.
  /// Usage int32_t r = SignExtend32<5>(x);
  template <unsigned B> inline int32_t SignExtend32(uint32_t x) {
    return int32_t(x << (32 - B)) >> (32 - B);
  }
  
  /// \brief Sign extend number in the bottom B bits of X to a 32-bit int.
  /// Requires 0 < B <= 32.
  inline int32_t SignExtend32(uint32_t X, unsigned B) {
    return int32_t(X << (32 - B)) >> (32 - B);
  }
  
  /// SignExtend64 - Sign extend B-bit number x to 64-bit int.
  /// Usage int64_t r = SignExtend64<5>(x);
  template <unsigned B> inline int64_t SignExtend64(uint64_t x) {
    return int64_t(x << (64 - B)) >> (64 - B);
  }
  
  /// \brief Sign extend number in the bottom B bits of X to a 64-bit int.
  /// Requires 0 < B <= 64.
  inline int64_t SignExtend64(uint64_t X, unsigned B) {
    return int64_t(X << (64 - B)) >> (64 - B);
  }
  
  /// \brief Subtract two unsigned integers, X and Y, of type T and return their
  /// absolute value.
  template <typename T>
  typename std::enable_if<std::is_unsigned<T>::value, T>::type
  AbsoluteDifference(T X, T Y) {
    return std::max(X, Y) - std::min(X, Y);
  }
  
  /// \brief Add two unsigned integers, X and Y, of type T.
  /// Clamp the result to the maximum representable value of T on overflow.
  /// ResultOverflowed indicates if the result is larger than the maximum
  /// representable value of type T.
  template <typename T>
  typename std::enable_if<std::is_unsigned<T>::value, T>::type
  SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) {
    bool Dummy;
    bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
    // Hacker's Delight, p. 29
    T Z = X + Y;
    Overflowed = (Z < X || Z < Y);
    if (Overflowed)
      return std::numeric_limits<T>::max();
    else
      return Z;
  }
  
  /// \brief Multiply two unsigned integers, X and Y, of type T.
  /// Clamp the result to the maximum representable value of T on overflow.
  /// ResultOverflowed indicates if the result is larger than the maximum
  /// representable value of type T.
  template <typename T>
  typename std::enable_if<std::is_unsigned<T>::value, T>::type
  SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) {
    bool Dummy;
    bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
  
    // Hacker's Delight, p. 30 has a different algorithm, but we don't use that
    // because it fails for uint16_t (where multiplication can have undefined
    // behavior due to promotion to int), and requires a division in addition
    // to the multiplication.
  
    Overflowed = false;
  
    // Log2(Z) would be either Log2Z or Log2Z + 1.
    // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z
    // will necessarily be less than Log2Max as desired.
    int Log2Z = Log2_64(X) + Log2_64(Y);
    const T Max = std::numeric_limits<T>::max();
    int Log2Max = Log2_64(Max);
    if (Log2Z < Log2Max) {
      return X * Y;
    }
    if (Log2Z > Log2Max) {
      Overflowed = true;
      return Max;
    }
  
    // We're going to use the top bit, and maybe overflow one
    // bit past it. Multiply all but the bottom bit then add
    // that on at the end.
    T Z = (X >> 1) * Y;
    if (Z & ~(Max >> 1)) {
      Overflowed = true;
      return Max;
    }
    Z <<= 1;
    if (X & 1)
      return SaturatingAdd(Z, Y, ResultOverflowed);
  
    return Z;
  }
  
  /// \brief Multiply two unsigned integers, X and Y, and add the unsigned
  /// integer, A to the product. Clamp the result to the maximum representable
  /// value of T on overflow. ResultOverflowed indicates if the result is larger
  /// than the maximum representable value of type T.
  /// Note that this is purely a convenience function as there is no distinction
  /// where overflow occurred in a 'fused' multiply-add for unsigned numbers.
  template <typename T>
  typename std::enable_if<std::is_unsigned<T>::value, T>::type
  SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) {
    bool Dummy;
    bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy;
  
    T Product = SaturatingMultiply(X, Y, &Overflowed);
    if (Overflowed)
      return Product;
  
    return SaturatingAdd(A, Product, &Overflowed);
  }
  
  } // namespace llvm
  
  #endif
  